Is there any way I could block Android Apps for example Instagram from accessing the Internet, using the SQUID software or something similar on my Personal Computer?
If you have access to the WiFi Router you can block traffic and/or mac address. there are custom firmware for some router models like DD-WRT or Open-WRT. But the phone still can by-pass via mobile data.
Filter rules are complicated and may have unwanted effects. This is just a example
"Instagram" uses TCP protocol for communication.
TCP traffic analysis
Remote tcp port(s): 443, 80.
HTTP traffic analysis
HTTP traffic is found in Instagram's traffic.
Host(s) being connected(regular expression): ^..ak.instagram.com, ^..cdninstagram.com.
TLS traffic analysis
TLS connections are found in Instagram's traffic.
TLS Host(s) being connected(regular expression): instagram.com.
How to block Instagram?
Block the listed ports to block Instagram.
Block the listed http and tls domains to block Instagram.
Setup a content filter(ie: WFilter), which can block Instagram via signature